MR Imaging can be used to detect both physical structure within the body and tissue function and viability. One imaging technique of particular interest for use with patients with brain, heart or liver damage, e.g. as a result of stroke, tumours, infarct, etc., is termed perfusion imaging.
In this technique, a bolus of an MR contrast agent (e.g. a gadolinium chelate such as those marketed as Omniscan® or Magnevist® by Amersham and Schering) is administered into the patient's vascular system and MR images from the region of interest are collected for a period covering the transit of the contrast agent bolus through the tissue in the region of interest. To this end, fast image acquisition sequences, e.g. spin echo, gradient recall (GRASS or FLASH), echo planar (EPI), RARE, hybrid, half excitation, etc. are used. Such sequences and bolus administration of MR contrast agents for perfusion imaging are well known in the art (see for example “Biomedical Magnetic Resonance Imaging”, Ed. Wehrli et al, VCH, 1988).
In clinical practice, it is common for the perfusion image series to be inspected and the results to be assessed qualitatively.
However in many instances a quantified result, e.g. an absolute measurement of regional blood flow, regional blood volume, regional mean transit time, regional time of arrival and regional time to peak are desired (see for example Rempp et al, Radiology 193: 637-641 (1994) and Vonken et al, MRM 41: 343-350 (1999)).
Using classical tracer kinetic theory, dynamic MR perfusion images are analysed to extract the tissue residue function, r(t), for each voxel. From r(t), quantified values for the regional parameters mentioned above may be determined. However, the local contrast signals, c(t), which for T2* may be extracted from the ratio of MR signal intensity ratio at time t to MR signal intensity at time 0 (i.e. before contrast agent arrival at the tissue of interest) is a convolution of r(t) and an arterial input function v(t). Similar procedures are used to extract c(t) from T1 weighted images.
r(t) describes the fraction of contrast agent still present in a tissue region at time t and is thus a function dependent on the physiological parameters of the tissue, e.g. blood volume and mean transit time. v(t) describes how the contrast agent is delivered to the tissue voxel, and as such gives an impression of the vascular structure in the organ. Conventionally, v(t) is assumed to be invariant spatially, i.e. in determining ri(t) from ci(t) a voxel, i, independent value for v(t) is determined and ri(t) is determined by deconvolving ri(t)*v(t). Thus
            c      i        ⁡          (      t      )        =                    k        ·        ln            ⁢                          ⁢                                    s            i                    ⁡                      (            t            )                                                s            i                    ⁡                      (            o            )                                =                            r          i                ⁡                  (          t          )                    *              v        ⁡                  (          t          )                    (where k is a constant dependant on the parameters used in the imaging technique, and si(t) is the signal intensity for voxel i at time t).